Graph this system of equations and solve. $y = \dfrac{5}{3} x - 1$ $y = 3 x - 5$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
Explanation: The y-intercept for the first equation is $-1$ , so the first line must pass through the point $(0, -1)$ The slope for the first equation is $\dfrac{5}{3}$ . Remember that the slope tells you rise over run. So in this case for every $5$ positions you move up You must also move $3$ positions to the right. $3$ positions to the right. $5$ positions up from $(0, -1)$ is $(3, 4)$ Graph the blue line so it passes through $(0, -1)$ and $(3, 4)$ The y-intercept for the second equation is $-5$ , so the second line must pass through the point $(0, -5)$ The slope for the second equation is $3$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up You must also move $1$ positions to the right. $1$ position to the right. $3$ positions up from $(0, -5)$ is $(1, -2)$ Graph the green line so it passes through $(0, -5)$ and $(1, -2)$ The solution is the point where the two lines intersect. The lines intersect at $(3, 4)$.